This Exam FM sample reference tests Arithmetically Increasing Coupons. After subtracting the fixed components from 1,050.50, division by the increasing-annuity factor gives X = 7.54. The result agrees with the published answer key, choice A.
How to solve this Arithmetically Increasing Coupons question
Setup
Setup
Use a 3% half-year yield for the fourteen coupon dates. Decompose each coupon into a level 22.50 component plus an arithmetic increase of X per period.
j=0.06/2=0.03,n=14
Model
Model
Price equals the level coupon annuity, X times the increasing-annuity factor, and the discounted redemption amount 300.
1050.50=22.50a14∣j+X(Ia)14∣j+300v14
Compute
Compute
After subtracting the fixed components from 1,050.50, division by the increasing-annuity factor gives X = 7.54.
X=7.54
Answer
Answer
The calculation gives 7.54 for arithmetically increasing coupons, matching published choice A.
X=7.54(A)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B (10.04) does not match the checked arithmetically increasing coupons result (7.54); no distinct standard one-step error is identifiable.
CChoice C (22.37) does not match the checked arithmetically increasing coupons result (7.54); no distinct standard one-step error is identifiable.
DChoice D (34.49) does not match the checked arithmetically increasing coupons result (7.54); no distinct standard one-step error is identifiable.
EChoice E (43.98) does not match the checked arithmetically increasing coupons result (7.54); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: price of a five-year increasing-coupon research bond
A five-year research bond pays annual coupons of 30, 35, 40, 45, and 50, then redeems 1,000 with the fifth coupon. At a 4% annual effective yield, calculate the bond price.
A 965.44
B 985.00
C 998.26
D 1,016.92
E 1,032.60
Variant answer in brief
The direct discounted cash-flow sum is 998.26. The increasing-coupon bond is worth 998.26, selecting choice C.
Setup
Setup
Combine the final coupon with redemption and retain the arithmetic coupon pattern at the earlier dates.
CF=(30,35,40,45,1050),i=0.04
Model
Model
Discount each of the five cash flows at 4%; a level-coupon shortcut would discard the increases.
P=t=1∑5CFt(1.04)−t
Compute
Compute
The direct discounted cash-flow sum is 998.26.
P=998.255126
Answer
Answer
The increasing-coupon bond is worth 998.26, selecting choice C.
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